Numerical solution of second-order stochastic differential equations with Gaussian random parameters

Subject Areas : Ordinary differential equations

R. Farnoosh ¹ , H. Rezazadeh ² , A. Sobhani ³ , D. Ebrahimibagha ⁴

1 - School of Mathematics, Iran University of Science and Technology, 16844, Tehran, Iran
2 - School of Mathematics, Iran University of Science and Technology, 16844, Tehran, Iran
3 - School of Mathematics, Iran University of Science and Technology, 16844, Tehran, Iran
4 - Department of Mathematics, Center Branch, Islamic Azad university, Tehran, Iran

Received: 2013-09-16 Accepted : 2013-12-31 Published : 2014-01-01

Keywords: Linear equations system, damped harmonic oscillators with noise, multiplicative noise, Stochastic Differential Equation, Gaussian random variables,

Abstract :

In this paper, we present the numerical solution of ordinary differential equations(or SDEs), from each order especially second-order with time-varying and Gaussian randomcoefficients. We indicate a complete analysis for second-order equations in special case ofscalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differential equations system from this equation, it couldbe approximated or solved numerically by different numerical methods. In the case of linearstochastic differential equations system by Computing fundamental matrix of this system, itcould be calculated based on the exact solution of this system. Finally, this stochastic equation is solved by numerically method like Euler-Maruyama and Milstein. Also its Asymptoticstability and statistical concepts like expectation and variance of solutions are discussed.

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